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Calculus

The differential equation dy/dx=(x+1)/(x-2)
I. produces a slope field with horizontal tangents at x = −1
II. produces a slope field with vertical tangents at x = 2
III.produces a slope field with rows of parallel segments

a) I and II only
b) II only
c) III only
d) I only

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  1. clearly, for any constant value of x, dy/dx is constant.
    since x-2=0 when x=2, the slope field is vertical there
    to get rows of parallel segments, you need a constant value for y. But that means you need (x+1) = y(x-2), which has only one solution. SO, no rows of parallel segments.

    Looks like I and II only, right?

    You know, there are online sites for checking slope fields. One of them is

    https://www.desmos.com/calculator/p7vd3cdmei

    Just change the function and watch the screen.

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